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from itertools import permutations
from math import sqrt
from typing import List
"""
We shall say that an n-digit number is pandigital if it makes use of all the digits
1 to n exactly once. For example, 2143 is a 4-digit pandigital and is also prime.
What is the largest n-digit pandigital prime that exists?
"""
"""
All pandigital numbers except for 1, 4 ,7 pandigital numbers are divisible by 3.
So we will check only 7 digit panddigital numbers to obtain the largest possible
pandigital prime.
"""
def is_prime(n: int) -> bool:
"""
Returns True if n is prime,
False otherwise.
>>> is_prime(67483)
False
>>> is_prime(563)
True
>>> is_prime(87)
False
"""
if n % 2 == 0:
return False
for i in range(3, int(sqrt(n) + 1), 2):
if n % i == 0:
return False
return True
def compute_pandigital_primes(n: int) -> List[int]:
"""
Returns a list of all n-digit pandigital primes.
>>> compute_pandigital_primes(2)
[]
>>> max(compute_pandigital_primes(4))
4231
>>> max(compute_pandigital_primes(7))
7652413
"""
pandigital_str = "".join(str(i) for i in range(1, n + 1))
perm_list = [int("".join(i)) for i in permutations(pandigital_str, n)]
return [num for num in perm_list if is_prime(num)]
if __name__ == "__main__":
print(f"{max(compute_pandigital_primes(7)) = }")